The Karmapa, one of the most senior religious figures from Tibet, has urged Tibetans in China to end a spate of self-immolations and find other ways to challenge Beijing's policies.

Eleven monks, former monks and nuns have set fire to themselves in Sichuan, south-west China this year.

Many see the 25-year-old Karmapa as a possible successor to the Dalai Lama as the spiritual leader of exiled Tibetans. Both men have expressed deep sorrow at the deaths and blamed Chinese policies for the self-immolations.

The Karmapa praised the bravery and "pure motivation" of those involved, saying each case had filled his heart with pain.

"These desperate acts … are a cry against the injustice and repression under which they live," he said.

But he added: "I request the people of Tibet to preserve their lives and find other, constructive ways to work for the cause of Tibet."

"The situation is unbearably difficult, but in difficult situations we need greater courage and determination."

Drawing on both his religion and the wider challenges facing Tibetans he added: "Most of those who have died have been very young. They had a long future ahead of them, an opportunity to contribute in ways that they have now foregone. In Buddhist teaching life is precious. To achieve anything worthwhile we need to preserve our lives. We Tibetans are few in number, so every Tibetan life is of value to the cause of Tibet."

Until two years ago – when a monk died after setting fire to himself in Aba county, where most of the cases have occurred – the practice was unknown among clerics.

But since the start of a security clampdown provoked by the second case, in March this year, there has been a series of such immolations.

The Karmapa said that, like the Dalai Lama, he believed that the real source of the problem lay in the "desperate circumstances" facing Tibetans and that using force was counterproductive.

"Repressive measures can never bring about unity and stability," he said.

"I appeal to the Chinese leaders to heed Tibetans' legitimate demands and to enter into meaningful dialogue with them instead of brutally trying to achieve their silence."

Aba – and in particular its largest monastery, Kirti – remains under heavy security.

Exile sources in Dharamsala said two monks were arrested in the monastery in the last week and taken away for unknown reasons. The numbers have already dwindled from 2,500 monks at the start of the year to a few hundred, with many reportedly detained or sent home.

The sources also alleged that 200 officials were now based in the monastery, monitoring life there and interfering with day-to-day religious practices.

They said officials had renewed efforts to enforce rules that all under-18s must attend the government school, threatening families with fines of 3000 yuan per child – a large sum relative to local incomes – if their children had become monks or were studying at monastery schools.

Police and government officials in Aba said they knew nothing of the detentions or other restrictions.

The Chinese government has said Tibetans are free to practise their faith and accused the Dalai Lama of "terrorism in disguise" because he has led prayers for those who have set fire to themselves.

A foreign ministry official said last month that the spiritual leader was inciting further cases by glorifying those who had self-immolated. Beijing accuses the Dalai Lama of seeking to split Tibet from China, while he says he seeks meaningful autonomy.

Separately, the Associated Press reported that a man in Tibetan monks' robes set fire to himself in Kathmandu, Nepal on Thursday in protest at Chinese policies.

• This article was amended on 18 November 2011 because the original referred to the Karmapa as the Karmapa Lama. This has been corrected